# Learning Impact-Rich Rotational Maneuvers via Centroidal Velocity Rewards and Sim-to-Real Techniques: A One-Leg Hopper Flip Case Study

arXiv: https://arxiv.org/abs/2505.12222 · HTML: https://mlsanity.com/paper/2505.12222/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in RL for robot locomotion and manipulation, one of 15 directions in Deep reinforcement learning methods.
- Builds on 24 of its 35 references that are in the map.
- First posted on arXiv 18 May 2025.

## Placed in

- Deep reinforcement learning methods / [RL for robot locomotion and manipulation](https://mlsanity.com/deeprl/rl-for-robot-locomotion-and-manipulation/)

## Builds on (most cited first, 24 of 24)

- [Learning Quadrupedal Locomotion over Challenging Terrain](https://mlsanity.com/paper/2010.11251/) (2020)
- [Learning robust perceptive locomotion for quadrupedal robots in the wild](https://mlsanity.com/paper/2201.08117/) (2022)
- [Sim-to-Real: Learning Agile Locomotion For Quadruped Robots](https://mlsanity.com/paper/1804.10332/) (2018)
- [Learning Agile Robotic Locomotion Skills by Imitating Animals](https://mlsanity.com/paper/2004.00784/) (2020)
- [ANYmal Parkour: Learning Agile Navigation for Quadrupedal Robots](https://mlsanity.com/paper/2306.14874/) (2023)
- [Robot Parkour Learning](https://mlsanity.com/paper/2309.05665/) (2023)
- [Concurrent Training of a Control Policy and a State Estimator for Dynamic and Robust Legged Locomotion](https://mlsanity.com/paper/2202.05481/) (2022)
- [Learning Agile Skills via Adversarial Imitation of Rough Partial Demonstrations](https://mlsanity.com/paper/2206.11693/) (2022)
- [Barkour: Benchmarking Animal-level Agility with Quadruped Robots](https://mlsanity.com/paper/2305.14654/) (2023)
- [OPT-Mimic: Imitation of Optimized Trajectories for Dynamic Quadruped Behaviors](https://mlsanity.com/paper/2210.01247/) (2022)
- [Optimization-Based Control for Dynamic Legged Robots](https://mlsanity.com/paper/2211.11644/) (2022)
- [The MIT Humanoid Robot: Design, Motion Planning, and Control For Acrobatic Behaviors](https://mlsanity.com/paper/2104.09025/) (2021)
- [Learning-based legged locomotion; state of the art and future perspectives](https://mlsanity.com/paper/2406.01152/) (2024)
- [Stage-Wise Reward Shaping for Acrobatic Robots: A Constrained Multi-Objective Reinforcement Learning Approach](https://mlsanity.com/paper/2409.15755/) (2024)
- [A Learning Framework for Diverse Legged Robot Locomotion Using Barrier-Based Style Rewards](https://mlsanity.com/paper/2409.15780/) (2024)
- [Humanoid Whole-Body Locomotion on Narrow Terrain via Dynamic Balance and Reinforcement Learning](https://mlsanity.com/paper/2502.17219/) (2025)
- [Cafe-Mpc: A Cascaded-Fidelity Model Predictive Control Framework with Tuning-Free Whole-Body Control](https://mlsanity.com/paper/2403.03995/) (2024)
- [Identifying Terrain Physical Parameters from Vision -- Towards Physical-Parameter-Aware Locomotion and Navigation](https://mlsanity.com/paper/2408.16567/) (2024)
- [Contact-Implicit Model Predictive Control: Controlling Diverse Quadruped Motions Without Pre-Planned Contact Modes or Trajectories](https://mlsanity.com/paper/2312.08961/) (2023)
- [Two-Stage Learning of Highly Dynamic Motions with Rigid and Articulated Soft Quadrupeds](https://mlsanity.com/paper/2309.09682/) (2023)
- [Achieving Stable High-Speed Locomotion for Humanoid Robots with Deep Reinforcement Learning](https://mlsanity.com/paper/2409.16611/) (2024)
- [Online Friction Coefficient Identification for Legged Robots on Slippery Terrain Using Smoothed Contact Gradients](https://mlsanity.com/paper/2502.16843/) (2025)
- [On the Emergence of Whole-body Strategies from Humanoid Robot Push-recovery Learning](https://mlsanity.com/paper/2104.14534/) (2021)
- [Momentum-Aware Trajectory Optimization and Control for Agile Quadrupedal Locomotion](https://mlsanity.com/paper/2203.01548/) (2022)

## Abstract (arXiv)

Dynamic rotational maneuvers, such as front flips, inherently involve large angular momentum generation and intense impact forces, presenting major challenges for reinforcement learning and sim-to-real transfer. In this work, we propose a general framework for learning and deploying impact-rich, rotation-intensive behaviors through centroidal velocity-based rewards and actuator-aware sim-to-real techniques. We identify that conventional link-level reward formulations fail to induce true whole-body rotation and introduce a centroidal angular velocity reward that accurately captures system-wide rotational dynamics. To bridge the sim-to-real gap under extreme conditions, we model motor operating regions (MOR) and apply transmission load regularization to ensure realistic torque commands and mechanical robustness. Using the one-leg hopper front flip as a representative case study, we demonstrate the first successful hardware realization of a full front flip. Our results highlight that incorporating centroidal dynamics and actuator constraints is critical for reliably executing highly dynamic motions. A supplementary video is available at: https://youtu.be/atMAVI4s1RY